Objetivo
Non-linear phenomena constitute an intensively studied subject in modern applied mathematics and theoretical and mathematical physics. Integrable non-linear evolution equations represent an important field in non-linear phenomena. Solitons, i.e. the coherent structures described by these equations, are found in various areas of physics and applied mathematics from plasma physics and non-linear optics, solid state physics and hydrodynamics, to elementary particle theories and gravitation. Their technological applications, for instance in fibre optics, are also very promising.
Non-linear partial differential equations (PDEs) which possess the soliton properties are of great interest in mathematics. The inverse scattering spectral transform method discovered 25 years ago enables detailed analytical study of such equations. The famous Korteveg-de Vries, non-linear Schrödinger and sine-Gordon equations exemplify the best known soliton equations with a great variety of applications. The inverse spectral transform method is applicable to a very broad class of non-linear evolution equations in 1 + 1 and 2 + 1 dimensions. Important results have been obtained in the field of the multidimensional integrable systems, which are worth additional study.
The development of methods to construct and solve multidimensional soliton PDEs is one of the main goals of the project. This includes, in particular, the multidimensional extensions of the inverse spectral transform, of the dressing method and of the direct linearization method. Different types of exact solutions, like the exponentially localized solutions, for multidimensional integrable equations will be studied together with their applications. An essential aim of this project is to investigate the nature of the integrability, its universality and wide applicability and its connection with the symmetry properties for both discrete and continuous systems. This investigation will result in a group theoretical classification of integrable non-PDEs and systems.
Another goal of the project is to study interrelations between multidimensional integrable equations and the theory of surfaces, their integrable deformations and the integrable motions of curves, modeling the variety of non-linear phenomena which involve interfaces, boundaries and lines. The project includes also the study of discrete systems and cellular automata and their application in information theory. Applications of the integrable systems in modern quantum field theory and statistical physics will also be studied.
Tema(s)
Convocatoria de propuestas
Data not availableRégimen de financiación
Data not availableCoordinador
73100 Lecce
Italia